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REVIEW 4 major objections 6 minor 80 references

Universal relation between residual resistivity and A coefficient in correlated metals

T0 review · 4 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read In correlated metals, residual resistivity is not correlation-independent: it grows linearly with the A coefficient, controlled by chemical-potential disorder.

desk verdict New κ-STFx data show a real ρ0–A correlation, but the 'universal' claim rests on fitting the same σ_μ² it is supposed to explain. read the letter →

arxiv 2508.21759 v1 pith:6WDUIDUU submitted 2025-08-29 cond-mat.str-el cond-mat.mtrl-sci

Anna Yu. Efimova , Yohei Saito , Atsushi Kawamoto , Martin Dressel , Louk Rademaker , Andrej Pustogow This is my paper
classification cond-mat.str-elcond-mat.mtrl-sci PACS 71.27.+a72.10.-d
keywords residualresistivityAcoefficientFermiliquidchemicalpotentialfluctuationschargepuddlesMotttransitioncorrelatedmetalsKadowaki-Woodsrelation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper challenges the textbook assumption that the residual resistivity ρ0 of a metal is a purely disorder-controlled quantity, untouched by electron-electron interactions. It establishes that in correlated metals ρ0 contains a term proportional to the quadratic temperature coefficient A of the Fermi-liquid resistivity, ρ(T)=ρ0+AT². The mechanism is spatial randomness of the local chemical potential (charge puddles): averaging the local Fermi-liquid scattering rate over the puddle distribution shifts the zero-frequency scattering rate by A′σμ², which translates into ρ0 ∝ A σμ². The authors verify the relation on organic κ-STF salts under pressure at fixed disorder, and show the same linear scaling across other organics, Sr₂RuO₄, heavy-fermion compounds, and moiré MoTe₂/WSe₂. If true, it means mass enhancement and disorder are not separable in transport the way transport textbooks assume.

What carries the argument

The load-bearing object is the local chemical-potential (charge-puddle) distribution P(μ), with variance σμ². The argument assumes each spatial patch is a local Fermi liquid whose scattering rate τ⁻¹(ω−μ(r), T) is the global Fermi-liquid rate shifted by the local chemical potential; averaging over P(μ) produces an extra A′σμ² term in the zero-frequency scattering rate. Because A is proportional to A′, this extra term becomes ρ0 ∝ A σμ². The relation carrying the argument is ρ0 = ρ00 + (3/4π²) A σμ², with A identified with the mass enhancement via the Kadowaki-Woods relation A ∝ (m*/m)².

What would settle it

Directly image the local chemical-potential landscape in one of the measured compounds (e.g., with scanning tunneling microscopy or Kelvin probe force microscopy) while simultaneously measuring ρ0 and A on the same sample; if the variance σμ² extracted from such images does not match the variance inferred from the transport slope, or if regions with different interaction strength show different local A′, the mechanism is incomplete. A second check is to introduce disorder by x-ray irradiation in a controlled way: if the measured dρ0/dA does not increase with irradiation dose, the relation fail

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Extended reading notes

Core claim

The central claim is Eq. (6): ρ0 = ρ00 + (3/4π²) A σμ², where ρ00 is the disorder-only residual resistivity, A is the coefficient of the T² term in ρ(T)=ρ0+AT², and σμ² is the variance of chemical-potential fluctuations in the sample. Starting from the Fermi-liquid scattering rate τ⁻¹(ω,T)=τ⁻¹₀₀ + A′[ω²+(πT)²], the authors note that disorder need not act only as momentum scattering; it can also appear as smooth spatial patches with different local chemical potential μ(r). Within each patch the Fermi-liquid scattering rate is unchanged except that energy is measured from the local μ(r). Averaging over a symmetric distribution P(μ) leaves the ω² and T² terms intact but adds A′σμ² to the zero-f

Load-bearing premise

The calculation assumes that electron-electron interactions enhance the effective mass uniformly across the sample, and that disorder only shifts the local chemical potential without changing the local A′ coefficient or the shape of the puddle distribution; if the mass enhancement itself is spatially inhomogeneous, or the chemical-potential distribution is skewed, the clean proportionality ρ0 ∝ A can break down.

Editorial extensions

If this is right

  • At fixed disorder, approaching a Mott transition (increasing m*/m) makes ρ0 grow linearly with A, so the residual resistivity diverges with mass enhancement, changing how quantum criticality manifests in ρ(T) intercepts.
  • Tuning disorder by chemical substitution or irradiation changes the slope dρ0/dA through σμ², giving a practical way to quantify local chemical-potential disorder from transport data alone.
  • Pressure tunes correlation strength without changing the disorder potential; the linear relation holds across all tested families, indicating that the correlation-induced part of ρ0 is a universal feature of correlated metals.
  • The relation provides a new route to estimate the chemical-potential fluctuation variance σμ² from measured ρ0 and A, independent of microscopic imaging.
  • The conventional Drude-style cancellation that makes ρ0 independent of mass enhancement no longer applies; ρ0 and A must be analyzed together.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the chemical-potential fluctuation distribution is asymmetric rather than symmetric, the averaging would introduce additional odd-frequency terms, likely producing a measurable linear-in-T resistivity component or thermopower signature; this is a testable extension the paper does not develop.
  • The transport-only estimate of σμ² could be checked directly against scanning tunneling microscopy or Kelvin probe force microscopy maps of the same material; a mismatch would reveal additional disorder mechanisms beyond local chemical-potential shifts.
  • In materials with nanoscale electronic phase separation, the local A′ coefficient should itself vary from patch to patch; in that case the simple linear ρ0–A slope would break down, which could be probed by comparing transport with spatially resolved probes.
  • In bad metals above the T² regime, the same averaging mechanism would add A′σμ² to the energy-dependent scattering background, potentially shifting the apparent Mott-Ioffe-Regel saturation scale.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript reports a new scaling relation between the residual resistivity ρ0 and the Fermi-liquid T² coefficient A in correlated metals: ρ0 = ρ00 + (3/4π²) A σ_μ², where σ_μ² is the variance of local chemical-potential fluctuations. The authors present pressure-dependent resistivity data on κ-[(BEDT-STF)_x(BEDT-TTF)_{1−x}]₂Cu₂(CN)₃ at fixed disorder levels x = 0.00, 0.04, 0.12, showing that ρ0 increases linearly with A as pressure tunes the correlation strength. They derive Eq. (6) by averaging the FL scattering rate over a symmetric distribution of local chemical-potential shifts, and then compile literature data on other organic conductors, Sr₂RuO₄, heavy-fermion compounds, and a moiré system to claim universality of the relation. The central theoretical step is internally consistent, but the evidence presented for universality is weakened by the fact that σ_μ is extracted from the same (ρ0, A) data used for the comparison, and by several unaddressed model assumptions.

Significance. If established, Eq. (6) would provide a simple, experimentally useful connection between residual resistivity and mass enhancement, with implications for how disorder and correlations combine near Mott transitions. The design of the κ-STF experiment—tuning pressure at fixed chemical substitution—is a good way to separate correlation from disorder effects, and the observed linear trends in Fig. 2d are suggestive. The derivation is compact and the manuscript is clearly written. However, the universal claim is currently supported mainly by fits of a free parameter, not by a parameter-free prediction. Independent microscopic estimates of σ_μ, a justification of the averaging procedure, and an assessment of spatial inhomogeneity of A' are needed before the relation can be regarded as established.

major comments (4)
  1. [Eq. (6) and Fig. 4] The central relation is tested by fitting σ_μ² to the same (ρ0, A) data that is then plotted in Fig. 4. The solid lines in Fig. 4 are least-squares fits with σ_μ as a free slope, so the figure replays the extraction rather than providing a parameter-free test of Eq. (6). The authors should either predict σ_μ from a structural or chemical disorder model, extract it from an independent probe (STM, dielectric, NMR), or make an out-of-sample prediction. Without this, the 'universality' claim is not falsifiable from the data presented.
  2. [Main text, p.2 and Eq. (4)] The derivation assumes a spatially uniform A' and disorder entering only through Δμ(r). The paper states that BEDT-STF substitution 'also tunes the correlation strength U/W'. Consequently, the same randomness that produces Δμ(r) also causes spatial fluctuations of A'(r) and of the mass enhancement. If A'(r) fluctuates and is correlated with Δμ(r), the averaged residual resistivity becomes ρ0 − ρ00 ∝ ⟨A' Δμ²⟩, while the measured A is ∝ ⟨A'⟩. The extracted 'σ_μ²' is then an effective ratio, not the bare variance of chemical-potential fluctuations. Given that x = 0.12 already shifts the phase diagram, this mixing may be significant and should be quantified or explicitly modeled.
  3. [Methods, 'Chemical potential fluctuations' (Eq. (12))] The step from local scattering rates to the macroscopic resistivity is not justified. The manuscript averages local 1/τ and inserts this average into a homogeneous Kubo formula, which corresponds to one particular (series-like) combination of local resistivities. If instead one averages local conductivities—equally plausible for parallel puddles—the A'σ_μ² term does not appear at leading order. The measured resistivity of an inhomogeneous sample depends on the spatial arrangement of the puddles; an effective-medium calculation is required to support Eq. (6) as the macroscopic resistivity. This is a load-bearing assumption for the central result.
  4. [Figs. 2 and 4 / App. B] No uncertainties are reported for the extracted ρ0 and A values, and the raw digitized data are not provided. For each κ-STF sample there are only about five to six pressure points, so the linearity of Fig. 2d should be quantified with confidence intervals and a measure of fit quality. For the literature data, the digitization procedures in App. B are qualitative, and no error propagation is given. Without these, the visual log-log collapse in Fig. 4 cannot be evaluated and the numerical values of σ_μ are not reproducible.
minor comments (6)
  1. [App. B, §3c] The stated pressures 'P = 0, 170, 350, 1000, and 2000 kbar' for κ-Br are unphysical; presumably the intended units are MPa or bar. Please correct.
  2. [Eq. (6)] The thermal-energy conversion between K and meV should be stated explicitly. If A is in μΩ cm K⁻² and σ_μ in meV, the numerical coefficient in Eq. (6) requires a k_B conversion factor; the current notation implicitly sets k_B = 1.
  3. [Fig. 2d] It would aid the reader to mark the pressure values on the ρ0 vs A plot, or to list them in the caption, since the same symbols are used for different pressures in panels (a)–(c).
  4. [App. B, Fig. 8 caption] The caption reads 'x = 0.012'; this should be 'x = 0.12'.
  5. [App. B, §4] Typo: 'three sumples' should be 'three samples'.
  6. [Fig. 4 caption] The notation κ-Cl, κ-SCN, and κ-Br is defined only in footnote [59]; the caption should include the full chemical formulas for readability.

Circularity Check

2 steps flagged · score 6.0 of 10

Central relation derived from an ansatz, but the claimed universality is not independently tested: ρ00 and σ_μ^2 are fit to the same (ρ0, A) data, so the Fig. 4 scaling replays the fits; the model additionally assumes a uniform A' although substitution also changes U/W.

  1. fitted input called prediction [Appendix B, captions of Figs. 5–8; main-text Eq. (6) and Fig. 4]
    "Solid symbols denote the measured data; solid lines are linear fits to ρ0 = ρ00 + (3/4π^2) σ_μ^2 A, where the fit parameters ρ00 and σ_μ^2 (the latter expressed in meV) are listed for each material in its respective panel."

    The 'universal relation' is introduced as a demonstration, but its two coefficients are obtained by fitting the very same (ρ0, A) pairs to Eq. (6). The figure plots ρ0 − ρ00 versus A after subtracting the fitted intercept, and the solid lines are the fitted slopes labeled as σ_μ^2. No independent measurement of σ_μ^2 or ρ00 is used. Thus the empirical support for Eq. (6) reduces to the statement that a linear fit with two free parameters per material can describe the data; the fitted parameter is then presented as the predicted chemical-potential variance. This is a fitted input called a prediction, not a parameter-free test.

  2. fitted input called prediction [Main text, p.2 (near Fig. 1) and Eq. (4)]
    "Note that, apart from changing the amount of disorder, partial substitution x of the sulfur-based BEDT–TTF molecules by selenium-containing BEDT–STF donors also tunes the correlation strength U/W [5, 6, 14–18]."

    Equation (4) assumes a single Fermi-liquid coefficient A' for every spatial patch, but the same chemical substitution used to create disorder also changes U/W and hence m*/m and A'. With a spatially varying A'(r), the averaged residual scattering term becomes <A'Δμ^2> rather than A'σ_μ^2, and the linear slope extracted from fits is <A'Δμ^2>/<A'>, not the bare chemical-potential variance. The σ_μ^2 values reported from the fits therefore absorb correlation inhomogeneity and cannot be identified with the model's claimed variance. This makes the relation non-identifying: the observed linear ρ0 − ρ00 vs A can be produced by U/W fluctuations even if chemical-potential fluctuations are absent.

full rationale

The derivation of Eq. (6) from Eqs. (2)–(5) is algebraically sound under the stated uniform-A' ansatz: averaging a locally shifted quadratic scattering rate over a symmetric distribution adds A'σ_μ^2 to the constant term, and converting A' to A yields the quoted factor 3/(4π^2). That theoretical step is not by itself circular. The circularity enters in the empirical validation. The paper claims to demonstrate universality by comparing with many materials, but the comparison is a set of linear fits with two free parameters per material, ρ00 and σ_μ^2, both obtained from the same (ρ0, A) data. Plotting ρ0 − ρ00 versus A then replays those fits; the quoted σ_μ^2 values are labels attached to the fitted slopes, not quantities measured independently. The Outlook even proposes future STM/KPFM experiments to test σ_μ^2, confirming that no independent determination exists. Moreover, the paper itself notes that substitution changes U/W, so the uniform-A' assumption is violated in the central organic series; the fitted slope can absorb correlation-strength fluctuations. The main result is therefore partially circular/underdetermined as an empirical claim, though the analytical form is a legitimate consequence of the ansatz. Score 6 reflects this partial circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 1 invented entities

The central claim rests on the FL form of the scattering rate, the Kubo formula, and a specific model of disorder as smooth, symmetric chemical-potential fluctuations with spatially uniform interaction strength. The disorder strength sigma_mu and the intercept rho00 are not derived but fitted per material.

free parameters (2)
  • rho00 (residual residual resistivity) = Varies per material, e.g., 0.1-0.5 mOhm cm for kappa-STFx
    Intercept of the linear fit of rho0 versus A for each sample or disorder level; represents disorder-only scattering.
  • sigma_mu (variance of chemical potential fluctuations) = 0.02, 0.4, 0.6, 1.8, 3, 8.2, 37 meV for materials in Fig. 4
    Slope of the linear fit of rho0 versus A divided by 3/4 pi^2; not independently measured, only inferred from the same data.
assumptions (5)
  • domain assumption Fermi-liquid quasiparticle scattering rate has the form tau^-1(omega,T) = tau00^-1 + A'(omega^2 + (pi T)^2) to leading order.
    Eq. 2 and Eq. A1; standard Landau Fermi-liquid theory.
  • domain assumption Conductivity is captured by the Kubo formula with a parabolic, single-band dispersion and a momentum-independent lifetime.
    Eq. 3 and Eq. 8; neglects band-structure and vertex corrections.
  • ad hoc to paper Chemical potential fluctuations are smooth on the scale over which FL correlations are established, so the local scattering rate is the FL form with shifted mu, and the distribution of Delta mu is symmetric.
    Eq. 4 and the discussion around Fig. 3; the symmetry assumption is required to remove the linear-in-omega term.
  • domain assumption For a given crystal, the disorder scattering rate tau00^-1 and the chemical-potential variance sigma_mu are independent of applied pressure; pressure only changes the correlation strength (U/W).
    Main text and Fig. 1; this is what allows the pressure runs to be interpreted as A-dependence at fixed disorder.
  • ad hoc to paper The FL coefficient A' is spatially uniform; only mu(r) varies, so the average of tau^-1(omega-mu(r),T) uses the same A' everywhere.
    Not stated explicitly; the averaging in Eq. 5 and A11 pulls A' out of the integral. Spatial variation of the mass enhancement would spoil the simple result.
invented entities (1)
  • Local chemical potential fluctuations (charge puddles) in correlated organic metals
    purpose: Provide the source of the rho0 proportional to A contribution by averaging the FL scattering rate over a distribution of local chemical potentials
    The paper infers sigma_mu from the slope of rho0 versus A; no direct STM or KPFM measurement of puddles is presented for these materials. Puddles are known in graphene, but their existence in kappa-STFx at the assumed scales is speculative.

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Pith. "Pith review of Universal relation between residual resistivity and A coefficient in correlated metals." pith.science (2026). https://pith.science/paper/6WDUIDUU

@misc{pith2026250821759,
  author       = {Pith},
  title        = {Pith review of: Universal relation between residual resistivity and A coefficient in correlated metals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6WDUIDUU}},
  note         = {Machine review of arXiv:2508.21759}
}
abstract

The effects of strong electronic correlations and disorder are crucial for emergent phenomena such as unconventional superconductivity, metal-insulator transitions, and quantum criticality. While both are omnipresent in real materials, their individual impacts on charge transport remain elusive. To disentangle their respective roles, we have independently varied the degree of randomness and the strength of electronic correlations -- by chemical substitution and physical pressure, respectively -- within the metallic phase nearby a Mott-insulating state. We find a distinct correlation dependence of the disorder-dependent residual resistivity $\rho_0$ in the Fermi-liquid regime $\rho(T)=\rho_0 + A T^2$, where $A\propto (m^{\star}/m)^2$ quantifies the electronic mass enhancement. Contrary to conventional expectations, we observe that at fixed disorder level $\rho_0$ grows linearly with $A$. This scaling can be understood in terms of chemical-potential fluctuations with variance $\sigma_\mu^2$, yielding $\rho_0 \propto A\,\sigma_\mu^2$. By comparing our findings to transport data on other organic Mott systems, oxides, heavy-fermion compounds, and moir\'e materials, we demonstrate that this new relation between residual resistivity and mass enhancement is a universal feature of correlated metals.

Figures

Figures reproduced from arXiv: 2508.21759 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. a-c shows our dc resistivity results for hydrostatic pressure applied in an oil pressure cell [7]. Supercon￾ductivity is found for all three samples [16]. Increasing pressure suppresses the insulating and superconducting behavior, stabilizing metallic resistivity at low tempera￾tures. Our analysis focuses on this metallic regime. Upon approaching low T, FL behavior with quadratic temper￾ature dependence is clearly v… view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: (a) of the Supplementary Information. 3. Moir´e MoTe2/WSe2 We included the resistivity data from Zhao et al. [58] on the moir´e heterobilayer MoTe2/WSe2. We used the publicly available data from their Fig. 3a, at fillings n = 1 + x, where the tuning parameter is the el…
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

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